The Hilbert matrix

$$\begin{aligned} {\mathcal {H}}_\lambda =\left( \frac{1}{n+m+\lambda }\right) _{n,m=0}^{\infty }, \quad \lambda \ne 0,-1,-2, \ldots \, \end{aligned}$$

generates a bounded linear operator in the Hardy spaces \(H^p\) and in the \(l^p\)-spaces. The aim of this paper is to study the spectrum of this operator in the spaces mentioned. In a sense, the presented investigation continues earlier works of various authors. More information concerning the history of the topic can be found in the introduction.

中文翻译：

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希尔伯特矩阵算子的谱

希尔伯特矩阵

$$ \ begin {aligned} {\ mathcal {H}} _ \ lambda = \ left（\ frac {1} {n + m + \ lambda} \ right）_ {n，m = 0} ^ {\ infty}， \ quad \ lambda \ ne 0，-1，-2，\ ldots \，\ end {aligned} $$

在Hardy空间\（H ^ p \）和\（l ^ p \）空间中生成有界线性算子。本文的目的是研究上述空间中该算子的频谱。从某种意义上说，本文的研究继续了各个作者的早期著作。在引言中可以找到有关该主题历史的更多信息。